Optimal. Leaf size=23 \[ \left (e^{5+e^{40}}+(-4+x)^2\right )^2 \left (x^2+x^3\right ) \]
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Rubi [B] time = 0.03, antiderivative size = 98, normalized size of antiderivative = 4.26, number of steps used = 3, number of rules used = 0, integrand size = 70, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} x^7-15 x^6+2 e^{5+e^{40}} x^5+80 x^5-14 e^{5+e^{40}} x^4-160 x^4+e^{2 \left (5+e^{40}\right )} x^3+16 e^{5+e^{40}} x^3+e^{2 \left (5+e^{40}\right )} x^2+32 e^{5+e^{40}} x^2+256 x^2 \end {gather*}
Antiderivative was successfully verified.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=256 x^2-160 x^4+80 x^5-15 x^6+x^7+e^{5+e^{40}} \int \left (64 x+48 x^2-56 x^3+10 x^4\right ) \, dx+e^{2 \left (5+e^{40}\right )} \int \left (2 x+3 x^2\right ) \, dx\\ &=256 x^2+32 e^{5+e^{40}} x^2+e^{2 \left (5+e^{40}\right )} x^2+16 e^{5+e^{40}} x^3+e^{2 \left (5+e^{40}\right )} x^3-160 x^4-14 e^{5+e^{40}} x^4+80 x^5+2 e^{5+e^{40}} x^5-15 x^6+x^7\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 22, normalized size = 0.96 \begin {gather*} \left (e^{5+e^{40}}+(-4+x)^2\right )^2 x^2 (1+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.56, size = 65, normalized size = 2.83 \begin {gather*} x^{7} - 15 \, x^{6} + 80 \, x^{5} - 160 \, x^{4} + 256 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{40} + 10\right )} + 2 \, {\left (x^{5} - 7 \, x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (e^{40} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 65, normalized size = 2.83 \begin {gather*} x^{7} - 15 \, x^{6} + 80 \, x^{5} - 160 \, x^{4} + 256 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{40} + 10\right )} + 2 \, {\left (x^{5} - 7 \, x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (e^{40} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.05, size = 71, normalized size = 3.09
method | result | size |
default | \({\mathrm e}^{2 \,{\mathrm e}^{40}+10} \left (x^{3}+x^{2}\right )+{\mathrm e}^{{\mathrm e}^{40}+5} \left (2 x^{5}-14 x^{4}+16 x^{3}+32 x^{2}\right )+x^{7}-15 x^{6}+80 x^{5}-160 x^{4}+256 x^{2}\) | \(71\) |
risch | \(x^{3} {\mathrm e}^{2 \,{\mathrm e}^{40}+10}+x^{2} {\mathrm e}^{2 \,{\mathrm e}^{40}+10}+2 x^{5} {\mathrm e}^{{\mathrm e}^{40}+5}-14 x^{4} {\mathrm e}^{{\mathrm e}^{40}+5}+16 x^{3} {\mathrm e}^{{\mathrm e}^{40}+5}+32 x^{2} {\mathrm e}^{{\mathrm e}^{40}+5}+x^{7}-15 x^{6}+80 x^{5}-160 x^{4}+256 x^{2}\) | \(87\) |
gosper | \(x^{2} \left (x^{5}+2 x^{3} {\mathrm e}^{{\mathrm e}^{40}+5}-15 x^{4}+{\mathrm e}^{2 \,{\mathrm e}^{40}+10} x -14 x^{2} {\mathrm e}^{{\mathrm e}^{40}+5}+80 x^{3}+{\mathrm e}^{2 \,{\mathrm e}^{40}+10}+16 \,{\mathrm e}^{{\mathrm e}^{40}+5} x -160 x^{2}+32 \,{\mathrm e}^{{\mathrm e}^{40}+5}+256\right )\) | \(88\) |
norman | \(x^{7}+\left (-14 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}-160\right ) x^{4}+\left (2 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}+80\right ) x^{5}+\left ({\mathrm e}^{2 \,{\mathrm e}^{40}} {\mathrm e}^{10}+16 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}\right ) x^{3}+\left ({\mathrm e}^{2 \,{\mathrm e}^{40}} {\mathrm e}^{10}+32 \,{\mathrm e}^{{\mathrm e}^{40}} {\mathrm e}^{5}+256\right ) x^{2}-15 x^{6}\) | \(93\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.35, size = 65, normalized size = 2.83 \begin {gather*} x^{7} - 15 \, x^{6} + 80 \, x^{5} - 160 \, x^{4} + 256 \, x^{2} + {\left (x^{3} + x^{2}\right )} e^{\left (2 \, e^{40} + 10\right )} + 2 \, {\left (x^{5} - 7 \, x^{4} + 8 \, x^{3} + 16 \, x^{2}\right )} e^{\left (e^{40} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 8.61, size = 75, normalized size = 3.26 \begin {gather*} x^7-15\,x^6+\left (2\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}+80\right )\,x^5+\left (-14\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}-160\right )\,x^4+\left (16\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}+{\mathrm {e}}^{2\,{\mathrm {e}}^{40}+10}\right )\,x^3+\left (32\,{\mathrm {e}}^{{\mathrm {e}}^{40}+5}+{\mathrm {e}}^{2\,{\mathrm {e}}^{40}+10}+256\right )\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.07, size = 88, normalized size = 3.83 \begin {gather*} x^{7} - 15 x^{6} + x^{5} \left (80 + 2 e^{5} e^{e^{40}}\right ) + x^{4} \left (-160 - 14 e^{5} e^{e^{40}}\right ) + x^{3} \left (e^{10} e^{2 e^{40}} + 16 e^{5} e^{e^{40}}\right ) + x^{2} \left (256 + e^{10} e^{2 e^{40}} + 32 e^{5} e^{e^{40}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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